Lorentz-Zygmund Spaces and Interpolation of Weak Type Operators

[摘要] The Lorentz-Zygmund spaces L^pa(log L)^α are a class of functionspaces containing as special cases the classical Lebesgue spaces L^p,the Lorentz spaces L^pa and the Zygmund spaces L^p(log L)^α. It isshown here that the Lorentz-Zygmund spaces provide the correctframework for the interpolation theory of weak type operators. Theinterpolation principles established here unify many classical resultsin harmonic analysis. In particular, there are applications to theFourier transform, the Hardy-Littlewood maximal operator, the Hilberttransform, and the Weyl fractional integrals.

[发布机构] University:California Institute of Technology;Department:Physics, Mathematics and Astronomy

[关键词] Mathematics